It has been noted by many practitioners (see, e.g., [1]}, [2]}, [3]}) that solving PINNs on too large an interval often results in convergence to a bad solution. The authors of [1]} advocate that the reason for this behavior is the difficulty of the optimization problem when the solution of a differential equation has a complex shape. Classical numerical solvers are less prone to this problem because they propagate the solution from the initial conditions towards the other end of the solution interval. The authors of [1]} propose to address this problem of PINNs in a way which is similar to classical solvers: they split the time domain onto sub-intervals and then sequentially solve the equations on each sub-interval using the predictions on the previous sub-interval as the initial conditions for the next one.
In this work, we extend this idea and propose an algorithm for automatic expansion of the solution interval for training PINNs. Our solution is based on training an ensemble of PINNs and using the ensemble agreement (confidence) as the criterion for expanding the solution interval to new areas.
